Inertial hybrid S-iteration algorithm for fixed point of asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space

Abstract

In this paper, we introduce an inertial hybrid S-iteration algorithm for two asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space. Strong convergence of the iterative scheme is established. Our results improve and extend many recent results in the literature.

Inertial hybrid algorithm for generalized mixed equilibrium problems, zero problems, and fixed points of some nonlinear mappings in the intermediate sense

“…Also, $$$ A $$$ satisfies () with $$$ \tau =\frac{1}{3} $$$ and $$$ 0\in {A}^{-1}(0) $$$. The performance of our proposed Algorithm () is compared with that of the algorithms of Husain and Asad [23] and Harbau and Ahmad [51] with $$$ {T}_1={T}_2=T $$$, which are as follows, respectively, $$$$ \left\{\begin{array}{l}{d}_0\in H,\\ {}{u}_n={T}_{b_n}{d}_n,\\ {}{s}_n=\left(1-{\varsigma}_n\right){u}_n+{\varsigma}_nT{u}_n,\\ {}{d}_{n+1}=T{s}_n,\kern0.30em \forall n\ge 0,\end{array}\right. $$$$ and …”

“…In this manuscript, we consider more general problems than those considered by Suantai and Tiammee [50] and Harbaua and Ahmadb [51]. But in the second example, we wish to consider a special case of problems which can be handled by our Algorithm.…”

“…Also, T is nonexpansive with 0 ∈ F(T) and consequently satisfies (7) with V n , r, k n = 0, and T n = T ∀n ∈ N. Also, A satisfies (10) with 𝜏 = 1 3 and 0 ∈ A −1 (0). The performance of our proposed Algorithm ( 36) is compared with that of the algorithms of Husain and Asad [23] and Harbau and Ahmad [51] with T 1 = T 2 = T, which are as follows, respectively,…”